Process for the determination of an assembly having isotropic oblique reflection in an extensive spectral region and assemblies obtained by this process

ABSTRACT

A reflecting assembly for polarized white light includes at least one mirror associated with a birefringent compensator preventing the reflected light from having a large phase anisotropy. The mirror or mirrors are metallic and covered with a protective silica layer having a geometric thickness of from 0 to about 400A. The birefringent compensator is a crystalline plate of predetermined thickness depending upon the thickness of the protective layer. Known compensators may be used in place of the birefringent plate.

United States Patent [191 Ferray [22] Filed: Oct. 24, 1973 [2]] App].No.: 409,160

[30] Foreign Application Priority Data Nov. 20, 1972 France 72.41106[52] US. Cl. 350/147; 350/157; 350/159 [51] Int. Cl. G02b 5/30 [58]Field of Search 350/147, 157, 159

[4 1 July 8,1975

[56] References Cited UNITED STATES PATENTS 2,464,141 3/1949 Maier350/3l0 3,774,986 ll/l973 Bourgoin 350/l57 Primary ExaminerAlfred E.Smith Assistant Examiner-Michael J. Tokar Attorney, Agent, orFirm-Cameron, Kerkam, Sutton, Stowell & Stowell [57] ABSTRACT Areflecting assembly for polarized white light includes at least onemirror associated with a birefringent compensator preventing thereflected light from having a large phase anisotropy. The mirror ormirrors are metallic and covered with a protective silica layer having ageometric thickness of from 0 to about 400A. The birefringentcompensator is a crystalline plate of predetermined thickness dependingupon the thickness of the protective layer. Known compensators may beused in place of the birefringent plate.

7 Claims, 9 Drawing Figures PATENI'EU JUL 1 5 SHEET NOE 88 N3 8? 8a 8 8gm 8N 8; x 2 88 R8 8% 8% 8 0 83 88 mg C NE ON :N R8 8d 85 Q8 Q 1 8 08 m88*? 8*. 8 0 $8 8 88 c 88 88 88 88 88 88 8Q 8822 Yul 08 .3 m8 8 Q8 Q8 Qm1 ..+.8+.Nm+ 8 8 8 $5 083 58 188283 83 a 8 -0 8 t N6 0 mm on? 887. 8888 88 88 88 88 2F 2 PATENTEDJUL 3.893; 749

SHEET 2 FIG:3

Aownm Z25 PROCESS FOR THE DETERMINATION OF AN ASSEMBLY HAVING ISOTROPICOBLIQUE REFLECTION IN AN EXTENSIVE SPECTRAL REGION AND ASSEMBLIESOBTAINED BY THIS PROCESS The present invention relates to a process forthe determination of a reflecting assembly which does not affect thestate of polarization of an oblique incident wave, in an extensivespectral region. It likewise relates to the assemblies having isotropicoblique reflection thus obtained.

The invention applies in particular to all instruments using polarizedlight when it is necessary to bend the beam for reasons of space. Thisis particularly the case in modern optical microscopes using polarizedlight, in which it is an advantage to introduce auxiliary systems suchas zoom or a pupillary relay between the objective and the eye-piece,without increasing the height of the instrument as a result. Up to now,it has been impossible to bend the beam without disturbing the state ofpolarization of the incident wave.

Actually, it is known that any oblique reflection of a polarized wave ona metallic surface is anisotropic. This is due to the inequality of thereflection coefficients corresponding to the states of polarizationparallel (polarizatiomp) and perpendicular (polarizationzs) to the planeof incidence. These coefficients generally have a complex expression ofthe form re" and may differ either by their modulus r or by their phaseqb. The inequality in the moduli leads to a rotation of the direction ofincident polarization which can easily be com pensated by rotation ofthe polarizer, while the inequality in the phases leads to transforminga rectilinear incident vibration into an elliptical reflected vibration.When these two inequalities coexist, corresponding to a rectilinearincident vibration there is an elliptical reflected vibration, the majoraxis of which does not coincide with the direction of the incidentpolarization.

In practice, this anisotropy of phases is expressed by twoimpossiblities:

impossibility of obtaining an extinction between crossed polarizersplaced one at each side of a mirror and having any orientation;

impossibility of measuring, by compensation, the birefringence of anobject placed in front of a mirror.

Various partial solutions to this problem are known. For example, it ispossible to compensate a first mirror by a second, identical to thefirst, on condition that their planes of incidence are perpendicular.The vibration parallel to the plane of incidence of the first becomesperpendicular to that of the second, and vice versa; this solution,proposed by CAPDECOMME, has the disadvantage of complicating the opticalarrangement considerably and is not always compatible with the availablespace.

It is also possible to dispose, between two mirrors working under thesame conditions, a half-wave crystal plate orientated in such a mannerthat it permutes the vibrations parallel and perpendicular to the planeof incidence. In this case, however, the compensation is only effectivefor the wavelength for which the plate is half-wave, hence theimpossibility of working with complex light and more particularly withwhite light. In any case, this solution, like previous one, has thedisadvantage of having recourse to two mirrors or at least to an evennumber of mirrors.

Nor does a total-reflecting prism constitute a solution; it does nothave any anisotropy of amplitude but the anisotropy of phase isconsiderable (about 51 for a glass of incidence 1.6) and substantiallyconstant in the visible spectrum.

It is also known to compensate, for a given wavelength, the anisotropyof phase of any mirror or of a total-reflecting prism, by a birefringentcompensator; but this compensation is not valid in an extensive spectralregion and in particular in white light. This is the case, inparticular, with the conventional aluminium mirrors which are protectedby a coating of silica having a thickness of the order of I000 A.

FIG. 1 is a table of the values in degrees of the anisotropy of phasefor an aluminum mirror coated with silica having a thickness of aboutIOOOA',

FIG. 2 is a table of values of the coefficients of the index of aluminumand silver;

FIG. 3 is a series of curves showing in full line curves of thedifferences in phase depending on wave length for an aluminum mirrorreceiving a beam of polarized white light at an incidence of 45corresponding to thicknesses of the protective layer from O to 1020A andin broken lines curves relating to quartz plates of various thickness;

FIG. 4 is a table of values for a bare aluminum mirror showinganisotropy of phase, the anisotrophy of phase in degrees introduced by aquartz plate and the residue of compensation;

FIG. 5 is a series of curves over the visible spectrum of the value indegrees of the residue of compensation for a bare aluminum mirror;

FIG. 6 is a table of values similar to FIG. 4 for a bare silver mirror;

FIG. 7 is a table of values for an aluminum mirror covered with aprotective layer of silica A thick;

FIG. 8 is a diagrammatic showing of polarized light reflected from amirror and passing through a crystalline birefringent plate; and

FIG. 9 is a showing similar to that of FIG. 8 in which the crystallinebirefringent plate is replaced by an equivalent compensator.

The table of FIG. 1 gives, in its first line, the values in degrees ofthe anisotropy of phase introduced by such a mirror for an incidence of45 and for the whole of the visible spectrum. In order to retain zeroanisotropy in the middle of the spectrum, it would be necessary to use a60-micron-wave quartz plate which produces a birefringence of 360 forthis wavelength. The second line of the table indicates, in degrees, theanisotropy of phase introduced by this quartz plate depending on thewavelengths of the spectrum. The third line of the table gives thecompensation residue, that is to say the difference in phase existingafter reflection of the beam of the mirror and passage through thequartz plate. It will be seen that in fact here the birefringentcompensator only provides real compensation in a very narrow zone aboutthe middle of the spectrum; on the contrary, it increases the defect assoon as there is a very slight movement away from this medianwavelength. It would be the same if a precise correction were aimed aton another wavelength.

The object of the present invention is to permit the constitution of anassembly associating a birefringent compensator with one or moremirrors, so that this assembly can be used in polarized light in anextensive spectral region. The invention relates to a process for thedetermination of the characteristics of the elements of this assemblyand likewise relates to the assemblies thus constituted,

The invention applies to an assembly consisting of at least one metallicmirror, which may or may not be covered with a thin layer of transparentdielectric, with which there is associated a crystalline compensatordevice equivalent to a thin plate.

According to the invention, for a given incidence, the thickness of thedielectric layer of the mirror or mirrors and the thickness of thecompensating crystal plate are determined depending on one another,working out by calculation.

on the one hand the variation in the difference in the complexcoefficient phases of reflection on the mirror or mirrors, relating tothe polarization parallel to and to the polarization perpendicular tothe plane of incidence, and this for different thickness of thedielectric. depending on the wavelength, in the spectral region underconsideration.

on the other hand the variation, depending on the same wavelengths, inthe difference in the phases, relating to these two directions ofpolarization, introduced by the passage through the crystal plate, fordifferent thicknesses of the plate,

finally the variation, depending on the same wavelengths, in the residueof compensation for the differences in phase for each assemblyassociating in pairs a thickness of crystal plate and a thickness ofmirror dielectric, in such a manner that the respective differences inphase are equal in absolute value and of opposite sign for the medianwavelength of the spectral region under consideration,

the final selection of the pair of thicknesses being made taking intoconsideration the minimum thickness of dielectric compatible with themechanical behaviour of the mirror when this factor is determinant, ortaking into consideration the maximum permissible residue ofcompensation when the use of the mirror allows the correspondingthicknesses of dielectric to be accepted.

The invention will now be described in more detail and will beillustrated by four specific examples of embodiment.

First of all, it may be recalled that for a metallic mirror protected bya layer of dielectric, the reflection coefficient corresponding to astate of polarization p or s is expressed by the formula:

I l+rlr2e" *B in which:

r, (rp or rs) is the modulus of the complex reflection coefficient forthe polarization p or s. b (d p or d) s) is the phase of the complexreflection coefficient for the polarization p or s. r1, (rlp or rls) isthe real reflection coefficient airlayer for the polarization p or s,r2, (r or ra is the modulus of the complex reflection coefficientmetal-layer for the polarization p or s. a (up or as) is the phase ofthe complex reflection coefficient metal-layer for the polarization p ors. B=41r(d/)\)nl cos il with k wavelength Lil d thickness of the layerOn the other hand it is known that with 10 angle of incidence ii angleof refraction in the layer i2 complex angle of refraction in the metalThese angles being connected by the relationships :10 sin [0 nl sin ilM2 sin [2 in which n0 (real) index of the air n1 (real) index in thelayer n2 (complex) index in the metal 1 n -jk It should be noted thatthe complex index n -jk in a metal such as aluminium or silver is not anabsolutely constant data but may vary very substantially depending onthe method of producing the metallic layer. For the examples givenbelow, the coefficients of the index of aluminium and of silver had thevalues given in the table of FIG. 2.

Knowing the angle of incidence i0 and the optical characteristics of themetal and of the layer, it is there fore possible, for a given thicknessof layer and a given wavelength, to obtain the phase (bp and the phasetbs corresponding to the states of polarization p and s, and to deducetherefrom the difference in phases dip tbs introduced by the reflectionon the mirror. It is thus possible to prepare a network of curves givingthe differences in phase depending on different wavelengths of thespectral region under consideration, and for various thicknesses oflayer.

The graph of FIG. 3 gives, in full lines, such a network of curvesrelating to an aluminium mirror receiving a beam of polarized whitelight at an incidence of 45. The various curves correspond to variousthick ness of the protective layer of silica, varying from 0 (baremirror) to 1020 A, this last thickness corresponding to conventionalpractice for such protected mirrors.

On the other hand, it may be recalled that the anisotropy of phaseintroduced by a crystal plate is expressed by the formula:

in which:

D is the thickness of the crystal plate, is the wavelength of the light,

N,. is the extraordinary index of the crystal,

N is the ordinary index of the crystal.

If, in the first instance, the spectral variation in the difference inthe indices of the crystal is ignored, it will be seen that theanisotropy of phase varies substantially as the inverse of thewavelength, and for each thickness of crystal, the curve of theanisotropy of phase depend ing on the wavelength has a hyperbolic shape.

The graph of FIG. 3 gives, in broken lines, a network of curves relatingto quartz plates of various thickness.

It will be seen first of all in the graph of PK]. 3 that in order toobtain a compensation for anisotropy of phase which is valid throughoutthe spectral region under consideration, by the association of a mirrorand a crystal plate, it is necessary for the curves of difference inphase relating to the mirror and the plate to be as symmetrical aspossible in relation to the axis of the abscissae. If the thickness ofthe silica deposited on the mirror exceeds 400 A, or more generally ifthe optical thickness (product of the geometrical thickness by theindex) exceeds 600 A, the curve relating to the mirror assumes such ashape that the compensation cannot be effected over the whole of thevisible spectrum. This is what was already seen above for a conventionalaluminium mirror covered with a layer of I020 A of silica.

The examples which will now be given will enable the mode ofdetermination of the association of a mirror 10, silica coating 11 and acrystal plate 12 as generally indicated in FIG. 8 with a view toobtaining the improved correction of the anisotropy of phase to bebetter understood, bearing in mind the mechanical strength requirementsof the mirrors.

EXAMPLE I A bare aluminium mirror is used, that is to say not coveredwith dielectric. The table in FIG. 4 gives, in its first line, thevalues in degrees of the anisotropy of phase introduced by the mirrorunder an incidence of 45, for the whole of the visible spectrum. Thethickness of the quartz plate which brings a precise correction for themedian wavelength of the visible spectrum, namely about 5500 A will thenbe sought. The second line of the table indicates in degrees theanisotropy of phase introduced by this quartz plate 2.17 microns thick,and the third line of the table gives the residue of compensation, thatis to say the difference in phase existing after reflection of the beamon the mirror and passage through the quartz plate.

It will be seen that this residue of compensation remains particularlylow over the whole extent of the visi' ble spectrum. In fact the maximumdefect is only 0.86", in the extreme red, which corresponds to anoptical path of H420.

The residue of compensation varies with the angle of incidence, but itmay be noted that it always remains small. The graph of FIG. 5 gives,over the extent of the visible spectrum, the values in degrees of thisresidue of compensation for this same bare aluminium mirror compensatedby a quartz plate of 2.17 microns, and for incidences from 2230 to 60.

The compensation is all the better, the less the difference between theindices of the crystal varies depending on the wavelength. It is forthis reason that magnesium fluoride is even more suitable than quartz,and the last two lines of the table in FIG. 4 give on the one hand theanisotropy of phase introduced by a magnesium fluoride plate 1.68microns thick, which precisely corrects the bare aluminium mirror forthe median wavelength of the spectrum, and on the other hand the residueof compensation. It will be seen that here it is even less than in thecase of quartz.

There is no doubt that the use of a bare aluminium mirror is difficultand necessitates special precautions, particularly at the moment whenthe mirror is mounted in its mount and at the moment when it is cleaned.

EXAMPLE 2 This example is illustrated by the table of FIG. 6 and relatesto a bare silver mirror, without dielectric protection. As for theprevious example, the thickness D 3.92 microns of the quartz plate wasdetermined in such a manner as to ensure precise compensation for themedian wavelength of the spectrum. The third line of the table gives, indegrees, the residues of compensation. Here it will be seen thataluminium might be preferred to silver for the mirror because theresidues of compensation are ultimately greater than in the previousexample of a bare aluminium mirror.

EXAMPLE 3 This example is illustrated by the first part of the table ofFIG. 7 and relates to an aluminium mirror covered with a protectivelayer of silica I50 A thick, which corresponds to an optical thicknessof 220 A; it gives the residues of compensation here resulting from itsassociated with a quartz plate 3.39 microns thick. It will be seen thatthe residues of compensation are higher than in Example I but stillremain broadly acceptable for numerous application.

EXAMPLE 4 This example is illustrated by the second part of the table ofFIG. 7 and gives, under the same conditions as before, the residue ofcompensation resulting from the association of an aluminium mirrorcovered with 300 A of silica (optical thickness 440 A) with a quartzplate 4.45 microns thick.

Thus it will be seen that the residues of compensation increase at thesame time as the thickness of the protective layer of silica isincreased. The final selection will therefore be made depending on thepreponderant requirements in the intended application. If an attempt ismade to minimize the residual anisotropy of phase in the mirror andcompensating plate assembly it would be necessary to accept limitationof the protective dielectric layer to very low values, even to use abare mirror, which necessitates special conditions for mounting themirror in the instrument. On the other hand, if it is the mechanicalstrength of the mirror which is the preponderant element, the minimumthickness of dielectric to be deposited would be fixed first, thethickness of the compensating quartz plate would be determined, and thecorresponding residues of compensation could be deduced therefrom.

Everything which has been described previously has been presented in adetailed manner for greater clarity of the explanation. In reality, allthese calculations can be effected quickly and easily by a computer.

Needless to say, the invention is not strictly limited to the exampleswhich have been described but likewise covers the equivalent modes ofembodiment. Thus, instead of crystal plates, when their thickness isimpracticable, recourse may be had to a suitably adjusted compensator,for example of the Babinet Soleil type as generally indicated at 13 inFIG. 9. Similarly, although the examples described relate to thecorrection of a single mirror, it is likewise possible to compensate aplurality of mirrors by means of a single plate; in this case thethickness of the compensating crystal plate would be multiplied by thenumber of mirrors, as would the residue of compensation.

I claim:

1. Optical assembly for the oblique reflection of a beam of polarizedlight covering a wide spectrum of wave lengths comprising a planemetallic mirror, a protective layer of transparent dielectric on saidmirror having an optical thickness of between and 600A, the beam oflight impinging on and being reflected by the mirror and protectivelayer and crystalline birefringent compensating means receiving thereflected light having birefringent compensation equivalent to that of acrystalline plate having a thickness for which the anisotropy of phasescreated by said means compensates exactly for the anisotrophy of phasescreated by said mirror for the means wave length of the spectrum of thebeam of light.

2. Method of compensating for the anisotrophy of phases created by thereflection of a polarized beam of light covering a wide spectrum of wavelengths by a plane metallic mirror protected by a layer of transparentdielectric having a thickness of O to 600A, the steps of directing thereflected beam of light through a birefringent compensating crystallineplate, adjusting the thickness of the plate whereby the anisotrophy ofphases created by the plate compensates for the anisotro' phy of phasescreated by the mirror for the mean wave length of the spectrum of thebeam of light, determining the adjusted thickness of the plate bymeasuring the anisotrophy of phases created by the mirror as a functionof wave length, preparing a set of curves of the variation of theanisotrophy of phases of the birefringent plate as a function of thewave length and for a series of thicknesses for the plate and thenfinding the thickness of the plate from the curve providing exactcompensation for the mean wave length of the spectrum 3. Method ofcompensating for the anisotrophy of phases created by the reflection ofa polarized beam of light covering a wide spectrum of wave lengths by aplane metallic mirror protected by a layer of transparent dielectrichaving a thickness of O to 600A, the steps of directing the reflectedbeam of light through a birefringent compensating crystalline plate,adjusting the thickness of the protective layer as a function of thethickness of the plate whereby the anisotrophy of phases created by themirror compensates for anisotrophy of phases created by the plate forthe mean wave length of the spectrum of the beam light, determining theadjusted thickness of the layer by measuring the variation of theanisotrophy of phases of the plate as a function of wave length,preparing a set of curves of the variation of anisotrophy of phases forthe mirror as a function of wave length and for a series of thicknessesof the layer and then finding the thickness of the layer from the curveproviding exact compensation for the mean wave length of the spectrum,

4. An optical assembly as described in claim 1 for reflection at anangle of incidence of 45 of white polarized light, the mirror being barealuminum and the plate being a quartz plate having a thickness of2.241..

5. An optical assembly as described in claim 4, for the reflection at anangle of incidence of 45 of white polarized light, the mirror being barealuminum and the birefringent compensating means being a birefringentcompensator.

6. An optical assembly as described in claim I for the reflection at anangle of incidence of 45 of polarized white light, the mirror being barealuminum and the plate being a magnesium fluoride plate having athickness of L7 7. An optical assembly as described in claim 1 for thereflection at an angle of incidence 45 of white polarized light, themirror being bare aluminum and the birefringent compensating means beinga birefringent compensator.

1. Optical assembly for the oblique reflection of a beam of polarizedlight covering a wide spectrum of wave lengths comprising a planemetallic mirror, a protective layer of transparent dielectric on saidmirror having an optical thickness of between 0 and 600A, the beam oflight impinging on and being reflected by the mirror and protectivelayer and crystalline birefringent compensating means receiving thereflected light having birefringent compensation equivalent to that of acrystalline plate having a thickness for which the anisotropy of phasescreated by said means compensates exactly for the anisotrophy of phasescreated by said mirror for the means wave length of the spectrum of thebeam of light.
 2. Method of compensating for the anisotrophy of phasescreated by the reflection of a polarized beam of light covering a widespectrum of wave lengths by a plane metallic mirror protected by a layerof transparent dielectric having a thickness of 0 to 600A, the steps ofdirecting the reflected beam of light through a birefringentcompensating crystalline plate, adjusting the thickness of the platewhereby the anisotrophy of phases created by the plate compensates forthe anisotrophy of phases created by the mirror for the mean wave lengthof the spectrum of the beam of light, determining the adjusted thicknessof the plate by measuring the anisotrophy of phases created by themirror as a function of wave length, preparing a set of curves of thevariation of the anisotrophy of phases of the birefringent plate as afunction of the wave length and for a series of thicknesses for theplate and then finding the thickness of the plate from the curveproviding exact compensation for the mean wave length of the spectrum.3. Method of compensating for the anisotrophy of phases created by thereflection of a polarized beam of light covering a wide spectrum of wavelengths by a plane metallic mirror protected by a layer of transparentdielectric having a thickness of 0 to 600A, the steps of directing thereflected beam of light through a birefringent compensating crystallineplate, adjusting the thickness of the protective layer as a function ofthe thickness of the plate whereby the anisotrophy of phases created bythe mirror compensates for anisotrophy of phases created by the platefor the mean wave length of the spectrum of the beam light, determiningthe adjusted thickness of the layer by measuring the variation of theanisotrophy of phases of the plate as a function of wave length,preparing a set of curves of the variation of anisotrophy of phases forthe mirror as a functIon of wave length and for a series of thicknessesof the layer and then finding the thickness of the layer from the curveproviding exact compensation for the mean wave length of the spectrum.4. An optical assembly as described in claim 1 for reflection at anangle of incidence of 45* of white polarized light, the mirror beingbare aluminum and the plate being a quartz plate having a thickness of2.2 Mu .
 5. An optical assembly as described in claim 4, for thereflection at an angle of incidence of 45* of white polarized light, themirror being bare aluminum and the birefringent compensating means beinga birefringent compensator.
 6. An optical assembly as described in claim1 for the reflection at an angle of incidence of 45* of polarized whitelight, the mirror being bare aluminum and the plate being a magnesiumfluoride plate having a thickness of 1.7 Mu .
 7. An optical assembly asdescribed in claim 1 for the reflection at an angle of incidence 45* ofwhite polarized light, the mirror being bare aluminum and thebirefringent compensating means being a birefringent compensator.